On adaptive optimal control for hybrid systems

Although the Policy Iteration is one of effective algorithms to solve an optimal control problem for nonlinear systems, it is not clear whether this algorithm can be applied for hybrid systems or not. In this paper, properties of a conventional policy iteration for nonlinear hybrid systems is analyzed and it is shown that the policy iteration can be applied for hybrid systems whose impact manifolds depend on only states, and that it cannot be applied for hybrid systems whose impact manifolds depend on both states and inputs. Then, we show that policy iteration can be applied for such hybrid systems by augmenting the system's state by including the inputs into the states, and the effectiveness of the method is verified by simulations.